Jonckheere-Terpstra (JT) Test for Ordinal Responses — InferenceOrdinalJonckheereTerpstraTest • EDI

Two-arm Jonckheere-Terpstra (JT) rank test for an ordinal response — for two groups, this reduces to the Mann-Whitney $U$ statistic. The point estimate is the stochastic superiority probability, centered at 0 under the null: $\hat\beta_T = \widehat{\Pr}(Y_T > Y_C) + \tfrac{1}{2}\widehat{\Pr}(Y_T = Y_C) - \tfrac{1}{2}$, computed from category counts as $U/(n_T n_C) - 1/2$. Asymptotic inference ($compute_asymp_confidence_interval(), $compute_asymp_two_sided_pval()) uses the classical null variance of the Mann-Whitney $U$ statistic, $\mathrm{Var}(U) = n_T n_C (n_T+n_C+1)/12$ (no tie correction), matching clinfun::jonckheere.test()'s normal approximation. This class also provides an exact, permutation-distribution-based two-sided p-value via $compute_exact_two_sided_pval_for_treatment_effect() (exact_jonckheere_terpstra_pval_cpp), which does not rely on the normal approximation.

References

Jonckheere, A. R. (1954). "A Distribution-Free k-Sample Test Against Ordered Alternatives." Biometrika, 41(1-2), 133-145, doi:10.1093/biomet/41.1-2.133 ; Terpstra, T. J. (1952). "The Asymptotic Normality and Consistency of Kendall's Test Against Trend, When Ties Are Present in One Ranking." Indagationes Mathematicae, 14, 327-333.

Super class

Inference -> InferenceOrdinalJonckheereTerpstraTest

Methods

Public methods

InferenceOrdinalJonckheereTerpstraTest$new()
InferenceOrdinalJonckheereTerpstraTest$compute_estimate()
InferenceOrdinalJonckheereTerpstraTest$compute_estimate_with_bootstrap_weights()
InferenceOrdinalJonckheereTerpstraTest$compute_exact_two_sided_pval_for_treatment_effect()
InferenceOrdinalJonckheereTerpstraTest$compute_asymp_confidence_interval()
InferenceOrdinalJonckheereTerpstraTest$compute_asymp_two_sided_pval()
InferenceOrdinalJonckheereTerpstraTest$clone()

+ inherited public methods from Inference

`InferenceOrdinalJonckheereTerpstraTest$new()`

Uses the shared randomization two-sided p-value contract; see InferenceRand.

Initialize the JT test object for a completed design with an ordinal, uncensored response.

Usage

InferenceOrdinalJonckheereTerpstraTest$new(
  des_obj,
  model_formula = NULL,
  verbose = FALSE
)

Arguments

des_obj: A completed DesignSeqOneByOne object.
model_formula: Optional formula for covariate adjustment. If NULL (default), the formula from the design object is used and its pre-computed design matrix is reused. If a formula is provided, a new design matrix is constructed from the design's imputed covariates.
verbose: Whether to print progress.

`InferenceOrdinalJonckheereTerpstraTest$compute_estimate()`

Returns the estimated treatment effect: the stochastic superiority measure $\widehat{\Pr}(Y_T > Y_C) + \tfrac12\widehat{\Pr}(Y_T=Y_C) - \tfrac12$, computed from the Mann-Whitney $U$ statistic (see class documentation).

Usage

InferenceOrdinalJonckheereTerpstraTest$compute_estimate(estimate_only = FALSE)

Arguments

estimate_only: If TRUE, skip variance component calculations.

`InferenceOrdinalJonckheereTerpstraTest$compute_estimate_with_bootstrap_weights()`

Recomputes the JT superiority estimate under subject/block bootstrap weights: the weighted version of the same stochastic superiority quantity, $\sum_{i,j} w_i w_j\left(\mathbb{1}[y_{T,i} > y_{C,j}] + \tfrac12\mathbb{1}[y_{T,i}=y_{C,j}]\right) \big/ \sum_{i,j} w_i w_j - \tfrac12$, used by the Bayesian bootstrap and related weighted-resampling machinery. Always leaves the standard error unavailable (NA) regardless of estimate_only — this weighted path never computes the null-variance approximation.

Usage

InferenceOrdinalJonckheereTerpstraTest$compute_estimate_with_bootstrap_weights(
  subject_or_block_weights,
  estimate_only = FALSE
)

Arguments

subject_or_block_weights: Bootstrap weights at the subject/block level.
estimate_only: Present for interface parity; this method never computes variance components regardless of its value.

`InferenceOrdinalJonckheereTerpstraTest$compute_exact_two_sided_pval_for_treatment_effect()`

Returns the exact, permutation-distribution-based two-sided p-value (exact_jonckheere_terpstra_pval_cpp) — unlike $compute_asymp_two_sided_pval(), this does not rely on the normal approximation to the Mann-Whitney $U$ null distribution.

Usage

InferenceOrdinalJonckheereTerpstraTest$compute_exact_two_sided_pval_for_treatment_effect(

)

`InferenceOrdinalJonckheereTerpstraTest$compute_asymp_confidence_interval()`

Computes the asymptotic normal confidence interval, using the same Mann-Whitney $U$ null-variance approximation ($n_T n_C(n_T+n_C+1)/12$, no tie correction) as clinfun::jonckheere.test(); see class documentation.

Usage

InferenceOrdinalJonckheereTerpstraTest$compute_asymp_confidence_interval(
  alpha = 0.05
)

Arguments

alpha: The significance level (default 0.05).

`InferenceOrdinalJonckheereTerpstraTest$compute_asymp_two_sided_pval()`

Computes the asymptotic normal two-sided p-value, using the same $Z$-approximation as clinfun::jonckheere.test(); see class documentation and $compute_exact_two_sided_pval_for_treatment_effect() for the exact (non-approximate) alternative.

Usage

InferenceOrdinalJonckheereTerpstraTest$compute_asymp_two_sided_pval(delta = 0)

Arguments

delta: The null treatment effect (default 0).

`InferenceOrdinalJonckheereTerpstraTest$clone()`

The objects of this class are cloneable with this method.

Usage

InferenceOrdinalJonckheereTerpstraTest$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

set.seed(1)
x_dat <- data.frame(
  x1 = c(-1.2, -0.7, -0.2, 0.3, 0.8, 1.3, 1.8, 2.3),
  x2 = c(0, 1, 0, 1, 0, 1, 0, 1)
)
seq_des <- DesignSeqOneByOneBernoulli$new(n = nrow(x_dat), response_type = "ordinal",
  verbose = FALSE)
for (i in seq_len(nrow(x_dat))) {
  seq_des$add_one_subject_to_experiment_and_assign(x_dat[i, , drop = FALSE])
}
seq_des$add_all_subject_responses(as.integer(c(1, 2, 2, 3, 3, 4, 4, 5)))
infer <- InferenceOrdinalJonckheereTerpstraTest$
  new(seq_des, verbose = FALSE)
infer
#> <InferenceOrdinalJonckheereTerpstraTest>
#>   Inherits from: <Inference>
#>   Public:
#>     approximate_bayesian_bootstrap_distribution_beta_hat_T: function (...) 
#>     approximate_bootstrap_distribution_beta_hat_T: function (...) 
#>     approximate_jackknife_distribution_beta_hat_T: function (unit = "auto") 
#>     approximate_m_out_of_n_bootstrap_distribution_beta_hat_T: function (...) 
#>     approximate_rand_bootstrap_distribution_beta_hat_T: function (...) 
#>     approximate_randomization_distribution_beta_hat_T: function (r = 501, delta = 0, transform_responses = "none", show_progress = TRUE, 
#>     approximate_subsampling_distribution_beta_hat_T: function (...) 
#>     capabilities: function () 
#>     clone: function (deep = FALSE) 
#>     compute_asymp_confidence_interval: function (alpha = 0.05) 
#>     compute_asymp_two_sided_pval: function (delta = 0) 
#>     compute_bayesian_bootstrap_confidence_interval: function (...) 
#>     compute_bayesian_bootstrap_two_sided_pval: function (...) 
#>     compute_bootstrap_confidence_interval: function (...) 
#>     compute_bootstrap_two_sided_pval: function (...) 
#>     compute_estimate: function (estimate_only = FALSE) 
#>     compute_estimate_with_bootstrap_weights: function (subject_or_block_weights, estimate_only = FALSE) 
#>     compute_exact_confidence_interval: function (...) 
#>     compute_exact_two_sided_pval_for_treatment_effect: function () 
#>     compute_jackknife_bias_estimate: function (unit = "auto") 
#>     compute_jackknife_estimate: function (unit = "auto") 
#>     compute_jackknife_std_error: function (unit = "auto") 
#>     compute_jackknife_wald_confidence_interval: function (alpha = 0.05, unit = "auto") 
#>     compute_jackknife_wald_two_sided_pval: function (delta = 0, unit = "auto") 
#>     compute_m_out_of_n_bootstrap_confidence_interval: function (...) 
#>     compute_m_out_of_n_bootstrap_two_sided_pval: function (...) 
#>     compute_rand_bootstrap_confidence_interval: function (...) 
#>     compute_rand_bootstrap_two_sided_pval: function (...) 
#>     compute_rand_confidence_interval: function (alpha = 0.05, r = 501, pval_epsilon = 0.005, show_progress = TRUE, 
#>     compute_rand_two_sided_pval: function (r = 501, delta = 0, transform_responses = "none", na.rm = TRUE, 
#>     compute_subsampling_confidence_interval: function (...) 
#>     compute_subsampling_sensitivity: function (...) 
#>     compute_subsampling_two_sided_pval: function (...) 
#>     compute_wald_confidence_interval: function (alpha = 0.05) 
#>     compute_wald_two_sided_pval: function (delta = 0) 
#>     duplicate: function (verbose = FALSE, make_fork_cluster = FALSE) 
#>     get_analysis_data: function () 
#>     get_covariates: function () 
#>     get_design_object: function () 
#>     get_mod: function () 
#>     get_model_formula: function () 
#>     get_nonestimable_reason: function () 
#>     get_nonestimable_stage: function () 
#>     get_optimization_alg: function () 
#>     get_response: function () 
#>     get_response_type: function () 
#>     get_summary: function () 
#>     get_supported_bayesian_bootstrap_ci_types: function (...) 
#>     get_supported_bayesian_bootstrap_pval_types: function (...) 
#>     get_supported_bootstrap_ci_types: function (...) 
#>     get_supported_bootstrap_pval_types: function (...) 
#>     get_supported_rand_bootstrap_ci_types: function (...) 
#>     get_supported_rand_bootstrap_pval_types: function (...) 
#>     get_supported_testing_types: function () 
#>     get_treatment: function () 
#>     initialize: function (des_obj, model_formula = NULL, verbose = FALSE) 
#>     is_nonestimable: function (type = c("any", "estimate", "se")) 
#>     num_cores: active binding
#>     select_optimal_b_subsampling: function (...) 
#>     select_optimal_m_out_of_n_bootstrap: function (...) 
#>     set_custom_randomization_statistic_cpp: function (fn) 
#>     set_custom_randomization_statistic_function: function (custom_randomization_statistic_function) 
#>     set_optimization_alg: function (optimization_alg = NULL, allow_irls = private$optimization_alg_allow_irls, 
#>     set_seed: function (seed) 
#>     set_testing_type: function (testing_type = "wald") 
#>     supports: function (capability) 
#>     supports_rand_pval_for_incidence: function () 
#>   Private:
#>     X: -1.2 -0.7 -0.2 0.3 0.8 1.3 1.8 2.3 0 1 0 1 0 1 0 1
#>     active_resampling_operation: NULL
#>     allocate_resampling_sizes_by_stratum: function (...) 
#>     analyze_custom_randomization_statistic: function () 
#>     any_censoring: FALSE
#>     approximate_bayesian_bootstrap_statistics_beta_hat_T: function (...) 
#>     approximate_bayesian_jackknife_distribution_beta_hat_T: function (...) 
#>     approximate_bootstrap_statistics_beta_hat_T: function (...) 
#>     approximate_jackknife_distribution_beta_hat_T_private: function (...) 
#>     approximate_m_out_of_n_bootstrap_distribution_beta_hat_T_impl: function (...) 
#>     approximate_subsampling_distribution_beta_hat_T_impl: function (...) 
#>     assert_design_supports_randomization_draw: function (method_family) 
#>     assert_design_supports_resampling: function (method_family) 
#>     assert_design_supports_resampling_replay: function (method_family) 
#>     assert_exact_inference_params: function (type, args_for_type) 
#>     assert_jackknife_supported: function (unit = "auto") 
#>     assert_no_incidence_only_randomization_args: function (resp_type, type, args_for_type) 
#>     assert_valid_bootstrap_type: function (...) 
#>     bayesian_bootstrap_cache_key: function (...) 
#>     bayesian_bootstrap_ci_types: NULL
#>     bayesian_bootstrap_pval_types: NULL
#>     bayesian_bootstrap_sample_weights: function (...) 
#>     bca_ci_core: function (...) 
#>     bca_pval_core: function (...) 
#>     begin_rand_worker_reuse_session: function () 
#>     boot_distr_cache: NULL
#>     bootstrap_ci_types: NULL
#>     bootstrap_confidence_interval_extreme: function (...) 
#>     bootstrap_estimates_extreme: function (...) 
#>     bootstrap_extreme_ci_width_threshold: NULL
#>     bootstrap_extreme_estimate_threshold: NULL
#>     bootstrap_pval_types: NULL
#>     bootstrap_replication_stats: function (...) 
#>     bootstrap_sample_indices: function (...) 
#>     bootstrap_subset_inference: function (...) 
#>     brt_mc_control: NULL
#>     build_bayesian_bootstrap_context: function (...) 
#>     build_fast_randomization_worker_cache: function (prev_cache = NULL, preserve_cache_keys = character()) 
#>     build_jackknife_deletion_draws: function (...) 
#>     build_randomization_ci_search_bounds: function (inf_obj, r, alpha, transform_arg, permutations, ci_search_control, 
#>     build_randomization_distribution_cache_key: function (r, delta, transform_responses, permutations) 
#>     build_resampling_draw_from_units: function (...) 
#>     cache_nonestimable_estimate: function (reason = "not_estimable") 
#>     cache_nonestimable_se: function (reason = "standard_error_unavailable") 
#>     cached_X_full_for_reduced: NULL
#>     cached_design_matrix: NULL
#>     cached_harden_for_design_matrix: NULL
#>     cached_hardened_X_cov: NULL
#>     cached_j_treat_for_reduced: NULL
#>     cached_keep_for_reduced: NULL
#>     cached_reduced_X: NULL
#>     cached_values: list
#>     cached_vc_params: NULL
#>     cached_w_for_design_matrix: NULL
#>     check_bootstrap_replicate_deadline: function (...) 
#>     check_rand_bootstrap_ci_deadline: function (...) 
#>     check_randomization_ci_deadline: function (ci_search_control = NULL, label = "Randomization CI bisection") 
#>     ci_bayesian_bca: function (...) 
#>     ci_bca: function (...) 
#>     ci_calibrated_bootstrap: function (...) 
#>     ci_from_boot_distribution: function (...) 
#>     ci_smoothed_bootstrap: function (...) 
#>     ci_studentized: function (...) 
#>     ci_symmetric_studentized: function (...) 
#>     clear_fit_warm_start: function () 
#>     clear_likelihood_null_warm_cache: function () 
#>     clear_likelihood_test_eval_cache: function () 
#>     clear_nonestimable_state: function () 
#>     closed_form_ci_from_affine_null_draws: function (...) 
#>     compute_asymptotic_jt_components: function (estimate_only = FALSE) 
#>     compute_bayesian_bootstrap_distribution_with_reused_workers: function (...) 
#>     compute_bayesian_bootstrap_worker_estimate: function (...) 
#>     compute_bootstrap_distribution_with_reused_workers: function (...) 
#>     compute_bootstrap_worker_estimate: function (worker_state) 
#>     compute_bootstrap_worker_estimate_via_compute_treatment_estimate: function (...) 
#>     compute_brt_null_statistics_with_reused_workers: function (...) 
#>     compute_brt_null_statistics_with_se: function (...) 
#>     compute_ci_by_inverting_the_randomization_test_iteratively: function (r, l, u, pval_th, tol, transform_responses, lower, 
#>     compute_exact_confidence_interval_rand: function (type, alpha, args_for_type) 
#>     compute_exact_jt_components: function () 
#>     compute_exact_two_sided_pval_rand: function (type, delta, args_for_type) 
#>     compute_fast_rand_bootstrap_distr: function (y0_full, rand_bootstrap_draws, delta, transform_responses, 
#>     compute_fast_randomization_distr_via_reused_worker: function (y, permutations, delta, transform_responses, preserve_cache_keys = character(), 
#>     compute_jackknife_distribution_with_reused_workers: function (...) 
#>     compute_jackknife_summary: function (unit = "auto") 
#>     compute_m_out_of_n_bootstrap_confidence_interval_impl: function (...) 
#>     compute_m_out_of_n_bootstrap_two_sided_pval_impl: function (...) 
#>     compute_rand_bootstrap_ci_pval_cached: function (...) 
#>     compute_rand_bootstrap_distribution_with_reused_workers: function (...) 
#>     compute_randomization_ci_pval_cached: function (inf_obj, r, delta, transform_responses, permutations, 
#>     compute_randomization_distr_via_reused_worker_states: function (permutations, delta, transform_responses, actual_rand_cores, 
#>     compute_randomization_worker_estimate: function (worker_state) 
#>     compute_resampling_draw_distribution: function (...) 
#>     compute_reusable_bootstrap_worker_distribution: function (...) 
#>     compute_subsampling_confidence_interval_impl: function (...) 
#>     compute_subsampling_sensitivity_impl: function (...) 
#>     compute_subsampling_two_sided_pval_impl: function (...) 
#>     compute_subsampling_worker_estimate: function (...) 
#>     compute_treatment_estimate_during_randomization_inference: function (estimate_only = TRUE) 
#>     compute_two_sided_brt_pval_studentized: function (...) 
#>     compute_two_sided_brt_pval_with_sequential_mc: function (...) 
#>     compute_two_sided_pval_with_sequential_mc: function (t, r, delta, transform_responses, show_progress, permutations, 
#>     compute_two_sided_randomization_pval_band: function (t0s, t, conf_level) 
#>     compute_two_sided_randomization_pval_from_t0s: function (t0s, t) 
#>     compute_wald_confidence_interval_impl: function (alpha) 
#>     compute_wald_two_sided_pval_impl: function (delta) 
#>     compute_z_or_t_ci_from_s_and_df: function (alpha) 
#>     compute_z_or_t_two_sided_pval_from_s_and_df: function (delta) 
#>     create_bootstrap_worker_state: function () 
#>     create_design_backed_bootstrap_worker_state: function (...) 
#>     create_design_matrix: function () 
#>     create_reusable_bootstrap_worker: function (...) 
#>     current_bayesian_bootstrap_context: NULL
#>     current_bayesian_bootstrap_subject_or_block_weights: NULL
#>     dead: 1 1 1 1 1 1 1 1
#>     des_obj: DesignSeqOneByOneBernoulli, DesignSeqOneByOne, Design, R6
#>     des_obj_priv_int: environment
#>     effective_parallel_cores: function (operation, requested_cores = self$num_cores) 
#>     end_rand_worker_reuse_session: function () 
#>     ensure_mirai_daemons: function (n) 
#>     ensure_resampling_distribution_cache: function (operation) 
#>     estimate_bootstrap_worker: function (...) 
#>     evaluate_lightweight_custom_randomization_statistic: function (lightweight_custom_context, y, w, dead, cpp_fn_override = NULL) 
#>     evaluate_m_out_of_n_bootstrap_size: function (...) 
#>     evaluate_subsampling_size: function (...) 
#>     expand_bound: function (inf_obj, bound, est, r, transform_arg, permutations, 
#>     expand_rand_bootstrap_bound: function (...) 
#>     expand_subject_or_block_weights_to_row_weights: function (...) 
#>     extract_dollar_paths: function (expr) 
#>     finalize: function () 
#>     fit_warm_start: NULL
#>     fit_warm_start_enabled: TRUE
#>     fit_warm_start_fisher: NULL
#>     fit_warm_start_type: NULL
#>     fit_warm_start_weights: NULL
#>     fit_with_hardened_qr_column_dropping: function (X_full, fit_fun, fit_ok, required_cols = 1L) 
#>     fixed_covariate_keep_cache: NULL
#>     fork_cluster: NULL
#>     generate_exchangeable_resampling_draws: function (...) 
#>     generate_permutations: function (r) 
#>     generate_rand_bootstrap_draws: function (...) 
#>     get_X: function () 
#>     get_bootstrap_type: function (...) 
#>     get_brt_distribution_prefix: function (...) 
#>     get_cached_centered_resampling_pivot: function (...) 
#>     get_cached_resampling_distribution: function (operation, cache_key) 
#>     get_cluster_jackknife_ids: function (...) 
#>     get_compiled_cpp_stat: function () 
#>     get_complexity_tier: function () 
#>     get_degrees_of_freedom: function () 
#>     get_estimand_type: function () 
#>     get_exchangeable_units: function (...) 
#>     get_fit_warm_start: function (type = c("beta", "params")) 
#>     get_fit_warm_start_fisher: function (expected_dim = NULL) 
#>     get_fit_warm_start_for_length: function (type = c("beta", "params"), expected_length = NULL) 
#>     get_fit_warm_start_weights: function (expected_n = NULL) 
#>     get_likelihood_null_warm_state: function (key) 
#>     get_likelihood_test_eval_cache: function () 
#>     get_likelihood_test_eval_entry: function (testing_type, delta) 
#>     get_optimal_warm_start_config: function (expected_length, expected_fisher_dim = expected_length) 
#>     get_or_create_fork_cluster: function () 
#>     get_randomization_ci_seed_candidates: function (inf_obj, alpha) 
#>     get_randomization_distribution_prefix: function (r, delta, transform_responses, show_progress, permutations, 
#>     get_resampling_block_ids: function (...) 
#>     get_resampling_cluster_ids: function (...) 
#>     get_resampling_draw_contract: function (operation) 
#>     get_resampling_strata_ids: function (...) 
#>     get_standard_error: function () 
#>     get_supported_testing_types_impl: function () 
#>     get_w_signed: function (w) 
#>     harden: TRUE
#>     has_general_censoring: FALSE
#>     has_match_structure: FALSE
#>     has_private_method: function (method_name) 
#>     high_precision_confirm_and_refine_ci_bound: function (l, u, lower, r, transform_responses, permutations, 
#>     infer_original_se: function (...) 
#>     invert_ci_to_find_two_sided_pval_for_treatment_effect: function (delta = 0) 
#>     invert_rand_bootstrap_test_bisection: function (...) 
#>     is_KK: FALSE
#>     is_a_asymp: function () 
#>     is_a_rand_ci: function () 
#>     is_bernoulli_design: function () 
#>     is_resampling_control_condition: function (...) 
#>     jack_distr_cache: NULL
#>     jackknife_always_nonestimable: function () 
#>     jackknife_block_size_gt_one_unsupported: function (unit = "auto") 
#>     jackknife_cache_key: function (unit = "auto") 
#>     likelihood_null_warm_cache: NULL
#>     likelihood_test_delta_key: function (testing_type, delta) 
#>     lin_xm_m_vec: NULL
#>     lin_xm_structural: NULL
#>     load_bayesian_bootstrap_draw_into_worker: function (...) 
#>     load_bayesian_bootstrap_weights_into_worker: function (...) 
#>     load_bootstrap_draw_into_worker: function (...) 
#>     load_bootstrap_sample_into_design_backed_worker: function (...) 
#>     load_bootstrap_sample_into_worker: function (worker_state, indices) 
#>     load_m_out_of_n_bootstrap_draw_into_worker: function (...) 
#>     load_non_param_bootstrap_draw_into_worker: function (...) 
#>     load_rand_bootstrap_assignment_into_worker: function (...) 
#>     load_rand_bootstrap_draw_into_worker: function (...) 
#>     load_randomization_draw_into_worker: function (worker_state, draw, delta, transform_responses, setup, 
#>     load_randomization_perm_into_worker: function (worker_state, perm_w, delta, transform_responses, y_delta, 
#>     load_resampling_draw_into_worker: function (operation, worker_state, draw, ...) 
#>     load_subsampling_draw_into_worker: function (...) 
#>     m: NULL
#>     m_out_of_n_bootstrap_cache_key: function (...) 
#>     m_out_of_n_bootstrap_centered_pivot: function (...) 
#>     m_out_of_n_bootstrap_sample_indices: function (...) 
#>     mark_jackknife_nonestimable_if_block_unsupported: function (unit = "auto") 
#>     missing_bootstrap_ci: function (...) 
#>     model_formula: formula
#>     n: 8
#>     n_cpp_threads: function (n_work_items) 
#>     normalize_delta_for_cache: function (delta, resolution = NULL) 
#>     normalize_exact_inference_args: function (type, args_for_type = NULL, pval_epsilon = NULL) 
#>     normalize_jackknife_unit: function (unit = "auto") 
#>     normalize_likelihood_test_delta: function (delta) 
#>     normalize_randomization_ci_search_control: function (ci_search_control, r, pval_epsilon) 
#>     null_fit_warm_start_enabled: TRUE
#>     num_cores_override: NULL
#>     object_has_private_method: function (obj, method_name) 
#>     optimization_alg: NULL
#>     optimization_alg_allow_irls: FALSE
#>     optimization_alg_default: lbfgs
#>     p: NULL
#>     par_lapply: function (X, FUN, n_cores = self$num_cores, budget = 1L, show_progress = FALSE, 
#>     parallel_dispatch_policy: function (operation) 
#>     prob_T: 0.5
#>     pval_bayesian_bca: function (...) 
#>     pval_bca: function (...) 
#>     rand_boot_draws_counter: NULL
#>     rand_bootstrap_ci_conservative_count: NULL
#>     rand_bootstrap_ci_timeout_deadline: function (...) 
#>     rand_bootstrap_ci_types: NULL
#>     rand_bootstrap_draw_matrices: function (...) 
#>     rand_bootstrap_pval_types: NULL
#>     rand_bootstrap_transform_code: function (...) 
#>     reduce_design_matrix_preserving_treatment: function (X_full) 
#>     reduce_design_matrix_preserving_treatment_fixed_covariates: function (X_full) 
#>     reduce_design_matrix_preserving_treatment_matrix: function (X_full) 
#>     reduce_treatment_only_design_fast: function (X_full) 
#>     reduced_design_keep_cache: NULL
#>     renumber_match_ids: function (...) 
#>     requires_blocking_design: function () 
#>     resampling_centered_pval: function (...) 
#>     resampling_ci_from_centered_distribution: function (...) 
#>     resampling_effective_p: function (...) 
#>     resampling_error_to_na: function (...) 
#>     resampling_scaling_factor: function (...) 
#>     resampling_scaling_key: function (...) 
#>     resolve_dollar_path: function (expr) 
#>     resolve_jackknife_unit: function (unit = "auto") 
#>     resolve_resampling_size: function (...) 
#>     resolve_resampling_unit: function (...) 
#>     reusable_bootstrap_worker_enabled: TRUE
#>     run_rand_bootstrap_iteration: function (...) 
#>     run_rand_bootstrap_iteration_with_se: function (...) 
#>     run_randomization_iteration: function (thread_des_obj, thread_inf_obj, perm_idx, permutations, 
#>     sample_exchangeable_unit_ids: function (...) 
#>     seed: NULL
#>     select_optimal_b_subsampling_impl: function (...) 
#>     select_optimal_m_out_of_n_bootstrap_impl: function (...) 
#>     select_optimal_resample_size: function (...) 
#>     sequential_mc_band_excludes_threshold: function (t0s, t, threshold, conf_level) 
#>     sequential_mc_control_enabled: function (mc_ctrl) 
#>     set_cached_centered_resampling_pivot: function (...) 
#>     set_cached_resampling_distribution: function (operation, cache_key, value) 
#>     set_fit_warm_start: function (start, type = c("beta", "params"), fisher = NULL, weights = NULL, 
#>     set_likelihood_null_warm_state: function (key, delta, start) 
#>     set_likelihood_test_eval_entry: function (testing_type, delta, entry) 
#>     setup_randomization_template_and_shifts: function (delta, transform_responses, zero_one_logit_clamp = .Machine$double.eps) 
#>     shift_randomization_responses: function (y, w, delta, transform_responses, response_type, inverse = FALSE, 
#>     should_use_design_randomization_for_incidence: function () 
#>     should_use_zhang_incidence_randomization: function () 
#>     smart_cold_start_default: TRUE
#>     stable_signature: function (obj) 
#>     studentized_bootstrap_pivots: function (...) 
#>     studentized_interval_scale_unstable: function (...) 
#>     subsampling_cache_key: function (...) 
#>     subsampling_centered_pivot: function (...) 
#>     subsampling_sample_indices: function (...) 
#>     subset_permutations: function (permutations, indices) 
#>     supports_bayesian_bootstrap: function (...) 
#>     supports_design_randomization_draw: TRUE
#>     supports_design_resampling: TRUE
#>     supports_design_resampling_replay: TRUE
#>     supports_interval_or_left_censored_data: function () 
#>     supports_reusable_bootstrap_worker: function () 
#>     sync_randomization_worker_state: function (thread_des_obj, thread_inf_obj) 
#>     try_cached_reduced_design_keep: function (X_full, keep = private$reduced_design_keep_cache) 
#>     use_reusable_bootstrap_worker: function () 
#>     validate_bootstrap_worker_state: function (...) 
#>     verbose: FALSE
#>     w: 0 0 1 1 0 1 1 1
#>     warned_no_parallel: FALSE
#>     weighted_superiority: function (y_vals, w_vals, row_weights) 
#>     xm_m_vec: NULL
#>     xm_structural: NULL
#>     y: 1 2 2 3 3 4 4 5
#>     y_L: NA NA NA NA NA NA NA NA
#>     y_R: NA NA NA NA NA NA NA NA
#>     y_temp: 1 2 2 3 3 4 4 5